Winkler signed a minor-league contract with the White Sox on Thursday and was assigned to Triple-A Charlotte.

Winkler was reassigned to minor-league camp Wednesday.

Winkler agreed to a minor-league contract with the Rangers on Wednesday that includes an invitation to major-league camp.

Winkler was released by the Cubs on Saturday, Meghan Montemurro of the Chicago Tribune reports.

Winkler was designated for assignment by the Cubs on Tuesday, Russell Dorsey of the Chicago Sun-Times reports.

Winkler allowed four runs (three earned) while retiring just a single batter in Monday's loss to the Reds. He gave up two hits and three walks with no strikeouts.

Winkler (1-3) allowed three earned runs on three hits and one walk across 1.1 innings, taking the loss to the Brewers in Game 2 of Tuesday's doubleheader.

Winkler (1-1) allowed two runs on two hits in one-third of an inning, taking the loss versus Cincinnati on Sunday. He also hit two batters.

Winkler, who pitched a scoreless inning of relief with two strikeouts in Friday's loss to the Reds, has 31 strikeouts and a 1.23 ERA across 29.1 innings this season.

Winkler, who tossed two scoreless innings of relief in Wednesday's win over the Padres, has a 0.46 ERA across 19.2 innings this season.